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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the derivative of the following functions 'ab initio', that is, using the definition. x^4 |
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Answer» SOLUTION :Let `y=x^4` Then `dy/dx=lim_(deltaxto0)((x+DELTAX)^4-x^4)/(deltax)` `x^4+4X^3 cdot deltax+6x^2 cdot(deltax)^2` `=lim_(deltaxto0)(+4x(deltax)^3+(deltax)^4-x^4)/(deltax)` `=lim_(deltaxto0){4x^3+6x^2 cdot deltax+4x(deltax)^2+(deltax)^3}=4x^3` |
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| 2. |
If x is real , then the maximum value of (x^(2)+14x+9)/(x^(2)+2x+3) is |
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Answer» 2 |
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| 3. |
An ellipse of eccentricity (2sqrt2)/3 is inscribed in a circle and a point within the circle is chosen at random. Let the probability that this point lies outside the ellipse be p. Then the value of 105 p is |
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Answer» |
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| 5. |
Find differential equation of the curve y=ae^(3x)+be^(5x). |
| Answer» SOLUTION :PROJECTION of the POINT (1,2,3) on xy-plane (1,2,0). | |
| 6. |
int1/(1+e^(x))dx is equal to |
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Answer» `log_(e)((e^(X)+1)/e^(x))+C` |
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| 7. |
Let a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2y+c_2z+d_2=0be two planes, where d_1, d_2gt0. Then, origin lies in acute angle, If a_1a_2+b_1b_2+c_1c_2lt0 and origin lies in obtuse angle if a_1a_2+b_1b_2+c_1c_2gt0. Further point (x_1, y_1, z_1) and origin both lie either in acute angle or in obtuse angle. If ( a_1x_1+b_1y_1+c_1z_1+d_1)(a_2x_1+b_2y_1+c_2z_1+d_2)gt0. one of (x_1, y_1, z_1) and origin in lie in acute and the other in obtuse angle,If ( a_1x_1+b_1y_1+c_1z_1+d_1)(a_2x_1+b_2y_1+c_2z_1+d_2)lt0 Q. Given the planes x+2y-3z+5=0 and 2x+y+3z+1=0. If a point P(2, -1, 2). Then |
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Answer» O and P both LIE in acute angle between the planes |
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| 8. |
Prove that the product of the perpendicular fromthe foci on any tangent to the ellips (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1is equal to b^(2) |
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| 9. |
The slopes of the tangents drawn form (0,2) to the hyperbola 5x^(2)-y^(2)=5 is |
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Answer» `3, (-1)/(3)` |
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| 10. |
A number n is chosen atrandom from S = {1,2,3,…, 50} Let A = {n in S : n + (50)/(n) gt 27} B= { n in S :nisa prime } and C = { n in S : nis a square } . Then, correct order of their probabilities is |
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Answer» <P>`P(A) LT P(B) lt P(C) ` |
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| 11. |
In the following figure, identify co-initial vector |
| Answer» Solution :`VECA "and" VECD` co-INITIAL vectors because they have the same initial point. | |
| 12. |
Findthe differential equation of the family of straightlines y =mx+(a)/(m)when (i) m is the parameter (ii) a is the parameter (iii) a , m both are parameters |
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Answer» (II) m (III) 0 |
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| 13. |
The normal line to a given curve at each point (x,y) on the curve passes through the point (3,0). If the curve contains the point (3,4) then its equation is |
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Answer» `X^(2) + y^(2) + 6X - 7 = 0` |
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| 14. |
Evaluate the following integrals int (2x^2 + e^x) dx |
| Answer» SOLUTION :`INT (2x^2+e^x)DX = 2x^3/3 + e^x +C` | |
| 15. |
Let [.] denote G.I.F. and tge0 and S={(x,y):(x-T)^(2)+y^(2)leT^(2) where T=t-[t]}. Then which of the following is/are INCORRECT? |
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Answer» the point `(0,0)` does not belong to `S` for an `t` |
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| 16. |
A and B are independent events such that P(A cup B)=0.60 and P(A)= 0.2 then find P(B). |
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Answer» |
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| 17. |
From the set of all families having three children, a family is picked at random If the eldest child happens to be a girl, find the probability that she has two brothers. |
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Answer» Solution :A family is picked up at RAMDOM from a set of families having 3 CHILDREN. The eldest child happens to be a GIRL. We have to find the probability that she has two brother. LET G denotes a girl and B denotes a boy. `therefore P (B)=1/2,P(G)=1/2` P (BB | G ) =P(B) xx P (G)=1/2xx1/2=1/4` |
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| 18. |
If the equations x^(2)+ax+b=0 and x^(2)+bx+a=0 (a != b) have a common root, then a+b is equal to |
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Answer» -1 |
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| 19. |
A: In a Delta ABC, if A,B,C are in A.P. and triangle is equilateral cos A+2 cos B+ cos C=2 R: In a Delta ABC, if A,B,C are in A.P. and cos A+ cos B+ cos C=2 then the triangle is isosceles. |
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Answer» A is TRUE, R is true and R is CORRECT EXPLANATION of A |
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| 20. |
Find the area bounded by the curve x^(2)=4y and the line x=4y-2. |
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| 21. |
An isosceles triangle of wood of base 2a and height h is placed with its base on the ground vertex directly above. The triangle faces the sun whose altitude is 30^@. Then, the tangent of the angle at the apex of the shadow is |
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Answer» `(2ah)/sqrt3` Let BCE be the shadow of `triangleABC` such that E is the apex of the shadow. Clearly, DE is the height of the TRIANGULAR shadow. Let `2alpha` be the angle at the apex E of the shadow. Then, `tan ALPHA =a/(DE)`  Since the altitude of the sun is `30^@` . Therefore, `tan 30^@=(AD)/(DE)RARR 1/sqrt3=h/(DE) rArr DE=sqrt3h` `therefore tan alpha=a/(sqrt3h)` Now, `tan 2alpha=(2 tan alpha )/(1-tan^2 alpha ) rArr tan 2alpha =(2a//sqrt3h)/(1-a^2/(3h^2))=(2sqrt3ah)/(3h^2-a^2)` |
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| 22. |
If f:R rarrR defined by f(x+y)=f(x)+f(y)-xy-1 for all x, y in R and f(1)=1 then the number of solution of f(x)+f(y)-xy-1 for all x, y in R and f(1)=1 then the number of solutions of f(n)=n, n in N is |
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Answer» 1 |
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| 23. |
Volume of parallelogram whose adjacent sides are given by veca, vecb, vecb xx vecc is, |
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Answer» 18 `THEREFORE [VECAVECB xx vecc]=|{:(2,1,2),(1,-1,1),(-6,0,6):}|=-36` `therefore` Volume =36 |
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| 24. |
A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted. Then, another ball is drawn at random. What is the probability of second ball being blue ? |
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| 25. |
Let X be a random variable which takes values k with the probability kp. where k = 1, 2, 3, 4 and p in (0,1) . Then thestandard deviation of X is : |
| Answer» Answer :D | |
| 27. |
Following the party, Max and his friends decide to play a party game with cards. There are 20 cards arranged in a row on the table. Each card is showing a positive integer. On each player's turn, he allowed to take either the left most or right most card. This is done until all the cards are taken. The winner is the player who has the greatest sum of numbers on his/her cards. What should be Max’s first move so that he can win the game? The sequences are:A rarr 2111381256892110715171841618191B rarr12181348161753192116111218141569 |
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Answer» 1 from A and 9 from B |
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| 28. |
IF (a+b)^2=c^2+ab in a Delta ABC and if sqrt2 (sinA+ cos A)=sqrt3 then ascending order of angles A,B,C is |
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Answer» A,B,C |
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| 29. |
If1 , omega , omega^(2) are the cube roots of unity , then find the values of the following . [(a + b omega + c omega^(2))/(c + a omega + b omega^(2))] + [(a + b omega +c omega)/( b + c omega+a omega ^(2 ) ] ] |
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| 30. |
Statement I: Asymptotes of hyperbola 3x+4y =2 and 4x-3y =5 are bisectors of transverse and conjugate axes of hyperbola Statement II :Transverse and conjugate axes of hyperbola are bisectors of the asymptotes Then correct statement is |
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Answer» Both the statement are True and statement II is the CORRECT explanation of statement I. |
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| 31. |
Find the projection of the vector hat(i)+3hat(j)+7hat(k) on the vector 7hat(i)-hat(j)+8hat(k). |
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| 32. |
If int(sin^(2)x)/(1+sin^(2)x)dx=x-Ktan^(-1)(Mtanx)+C then |
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Answer» `M = (1)/(SQRT(2))` |
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| 33. |
If x = sin theta and y = cos p theta, then (1- x^(2)) y_(2) = |
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Answer» <P>`xy_(1) - p^(2)y` |
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| 34. |
Match the following |
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Answer» a, B, c, d |
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| 35. |
Pierrecompetes ina triathlonalonga courseas showninthe figurebelow, Hebeginsswimmingat startingpointS andswimsstraightacrossthe lake, getsonhisbicycleat stationA,bikesto stationB,and themrunsto finishinglineF.The judgesusea stopwatch torecordhis elapsedtimesoft_A,t_B andt_F hoursfrompointS to points A,B , andF, respectively.If thedistance, in miles, betweenpoints Sand Aalongthe racecourseis denotedby SA, thenwhatispierre 'saveragespeedfor thisrace, inmilesper hour? |
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Answer» `(SA )/(T_A)` |
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| 36. |
If the relation R be defined on the set A = {1,2,3,4,5}by R = {(a,b):|a^(2) -b^(2)| lt 8} . Then , R is given by ............. |
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Answer» |
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| 37. |
If a,b,c re in H.Pthen which one of the following is true |
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Answer» `(1)/(B-a)+(1)/(b-c) = (1)/(b)` |
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| 38. |
Match the following |
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Answer» a, b, c, d |
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| 39. |
Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(2),-ab]|=0 |
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Answer» Mutualism |
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| 40. |
Let a_(1), b_(1) = 8, a_(1 + 1) = a_(1) + (3)/(2) b_(1) and b_(1 + 1) = (1)/(2) b_(1) AA I = 1,2,3…… Let A_(i) be area of the loop formed by |x - a_(1)| + |y| = b_(1). If all the loops are plotted on the same X-Y plane, then the value of uu A_(1) is |
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Answer» `(512)/(3)` sq. units |
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| 41. |
Match the following |
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Answer» a, B, c, d |
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| 43. |
Evaluate the definite integrals int_(2)^(3)(dx)/(x^(2)-1) |
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| 44. |
If x^(2)y-x^(3)(dy)/(dx)=y^(4)cosx then x^(3)y^(-3) is equal to |
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Answer» `y^(3)(1+3 SIN X) = x^(3)` |
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| 45. |
S_(1) : int (x^(5))/(x^(2) + 1) dx = (x^(4))/(4) - (x^(2))/(4) - (x^(2))/(2) + log (x^(2) + 1) + c S_(1) int (sin^(6)x)/(cos^(8) x) dx = (1)/(7) tan^(7) x + c S_(3): int (x^(8))/(x^(6) +1) dx = (x^(3))/(3) -(1)/(3) tan^(-1)x^(3) + c Which of the above statements is /are false ? |
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Answer» `S_(1) and S_(2)` |
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| 47. |
What were the things being taken for granted by the people of Alsace? |
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Answer» TEACHERS of the school |
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| 48. |
underset(x to o)"Lt" ("cosec x"-1/x-x/6)/(x^(3))= |
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Answer» `1//120` |
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| 49. |
If PM is the perpendicular from P(2,3) onto the line x+y=3, then the coordinates of M are |
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Answer» `(2,1)` |
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| 50. |
Match the following |
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Answer» a, B, c, d |
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